We propose a procedure for conducting robust Bayesian inference in structural vector autoregressions (SVARs) whose parameters are not point identified. Partial identification could arise because the number of equality restrictions one can credibly impose is not sufficient for point identification and/or the restrictions come in the form of sign restrictions on the model’s parameters or on the impulse response functions. The procedure could for example be used to perform inference in “partially ordered” SVARs. The presence of partial identification makes Bayesian inference sensitive to the choice of prior: unlike for the point-identified case, the effect of the prior does not vanish asymptotically. In order to make inference robust to the choice of prior, we propose using a class of priors (ambiguous beliefs) for the non-identified aspects of the model and reporting the range of posterior means and posterior probabilities for, e.g., the impulse response function as the prior varies over the class. We argue that this posterior bound analysis is a useful tool to separate the information provided by the likelihood from the information provided by the prior input that cannot be updated by data.  The posterior bounds we construct asymptotically converge to the true identified set, which is an object of interest of frequentist inference in set-identified models. In terms of implementation, the posterior bound analysis is computationally simpler, and can accommodate a larger class of zero and sign restrictions than the frequentist confidence intervals proposed by Moon, Schorfheide, and Granziera (2013). Joint with Raffaella Giacomini.